Is the stair dimension for a half-turn staircase too small?

Difficult

No! For you, apparently not for everyone else.

half-turned stairway

That is probably a double-turned one? You come out on the side from which you entered the staircase?

Eye: 30 cm

And that is open? Or is it separated inside by a wall?

The architect now thinks the stair size is only a makeshift solution

It reads like that, yes. 100 cm gross, from which the handrail is deducted. You can't say much in general because it depends on the situation. If other walls stand inconveniently somewhere, risers restrict walkability, then the entire stairway can be unsatisfactory due to further limitations and its usefulness is questionable. One should consider that not only healthy and upright people with sturdy footwear use the stairs once a day, but also possibly children, bare feet, with laundry baskets, ladders under the arm, or a sleeping child over the shoulder. If you want to gain living space, there are other options available.

Especially since the 10 cm on the stairs make a world of difference, whereas in a room (unless you are trying to fit a very specific existing piece of furniture exactly into a niche), 10 cm actually don’t matter that much, or if it does matter, the planning was most likely a mess.

Yes, certainly a difficult compromise decision for us. A wider staircase takes up a lot of other space. The opinions help with the decision-making.

A wider staircase takes up a lot of other space.

10cm over what length? 2m. Then calculate well over a whole 0.2 sqm. How small is the house where 0.2 sqm per side is "a lot"?

With 0.2 m², it’s not going to be enough for our space situation. I will not justify myself either. Thank you.

With 0.2 m², it won’t be enough for our room situation. I will not justify myself either. Thank you.

Then not. There is nothing better than information to get a good answer. Unfortunately, you ask a striking question without background for those who are supposed to answer it.